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2.3 Applying Slope, Midpoint, and Length Formulas
You can use analytic geometry to determine properties of geometric shapes.
A graph can be helpful for understanding a problem and for checking whether answers are reasonable.
You can use different methods to solve the same problem. Solving a problem in two different ways lets you check your calculations.
Example 1. Determine the shortest distance from the point (5,-1) to the line y=2x+1. Round to the nearest tenth of a unit.
-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 1 0
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
x
y
Example 2. The vertices of ABCD are A (5,5), B(-3,-1), and C(1,-3). Determine whether ABCD
is a right triangle.
Example 3. Show that the median from the right angle of the triangle in Example 2 is half as long as the hypotenuse.
-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 1 0
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
x
y
